2.3.194 Problems 19301 to 19400

Table 2.961: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

19301

19334

\begin{align*} y-x y^{2}+\left (y^{2} x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}

7.273

19302

21096

\begin{align*} {x^{\prime }}^{2}-t x+x&=0 \\ \end{align*}

7.273

19303

25741

\begin{align*} y^{\prime \prime }&=y^{\prime } \\ \end{align*}

7.273

19304

8348

\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

7.276

19305

8452

\begin{align*} \left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\ y \left (1\right ) &= 10 \\ \end{align*}

7.281

19306

3608

\begin{align*} m v^{\prime }&=m g -k v^{2} \\ v \left (0\right ) &= 0 \\ \end{align*}

7.287

19307

12178

\begin{align*} y^{\prime }&=\frac {32 y x^{5}+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 y^{2} x^{4}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \\ \end{align*}

7.288

19308

6841

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\ \end{align*}

7.289

19309

21828

\begin{align*} y^{\prime }+4 y&=x^{2} \\ \end{align*}

7.289

19310

21100

\begin{align*} x&=t x^{\prime }+\frac {1}{x^{\prime }} \\ \end{align*}

7.290

19311

14520

\begin{align*} y-1+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

7.291

19312

8472

\begin{align*} y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}

7.292

19313

12028

\begin{align*} y^{\prime }&=-\frac {i \left (i x +x^{4}+2 y^{2} x^{2}+y^{4}\right )}{y} \\ \end{align*}

7.293

19314

20220

\begin{align*} x +y y^{\prime }+\frac {-y+y^{\prime } x}{x^{2}+y^{2}}&=0 \\ \end{align*}

7.293

19315

27074

\begin{align*} x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

7.293

19316

5159

\begin{align*} 2 y y^{\prime } x&=y^{2}+a x \\ \end{align*}

7.294

19317

1671

\begin{align*} x^{3} y^{\prime }&=2 y^{2}+2 x^{2} y-2 x^{4} \\ \end{align*}

7.296

19318

15835

\begin{align*} v^{\prime }&=-\frac {v}{R C} \\ \end{align*}

7.298

19319

24813

\begin{align*} x^{6} {y^{\prime }}^{3}-3 y^{\prime } x -3 y&=0 \\ \end{align*}

7.299

19320

15586

\begin{align*} y^{\prime }&=y^{2}-2 y \\ y \left (0\right ) &= 1 \\ \end{align*}

7.300

19321

3635

\begin{align*} y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\ \end{align*}

7.302

19322

22006

\begin{align*} y^{\prime }&=\frac {x \,{\mathrm e}^{x}}{2 y} \\ \end{align*}

7.302

19323

27770

\begin{align*} y^{\prime \prime } x +y \ln \left (1-x \right )&=0 \\ \end{align*}

Series expansion around \(x=0\).

7.302

19324

3662

\begin{align*} \left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right )&=2 \left (b -a \right ) y \\ \end{align*}

7.303

19325

19106

\begin{align*} y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\ \end{align*}

7.306

19326

6023

\begin{align*} x^{2} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

7.308

19327

12471

\begin{align*} x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}

7.308

19328

20105

\begin{align*} 6 y-4 \left (a +x \right ) y^{\prime }+\left (a +x \right )^{2} y^{\prime \prime }&=x \\ \end{align*}

7.308

19329

23102

\begin{align*} y^{\prime }+y&=0 \\ \end{align*}

7.308

19330

9974

\begin{align*} t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}

7.309

19331

1733

\begin{align*} 3 y x +2 y^{2}+y+\left (x^{2}+2 y x +x +2 y\right ) y^{\prime }&=0 \\ \end{align*}

7.312

19332

22630

\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}

7.312

19333

3644

\begin{align*} 2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\ \end{align*}

7.315

19334

11509

\begin{align*} y y^{\prime }-{\mathrm e}^{\frac {x}{y}} x&=0 \\ \end{align*}

7.316

19335

14507

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

7.320

19336

15372

\begin{align*} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1&=0 \\ \end{align*}

7.320

19337

3295

\begin{align*} y&=x +3 \ln \left (y^{\prime }\right ) \\ \end{align*}

7.321

19338

5251

\begin{align*} x \left (1-y^{2}\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\ \end{align*}

7.323

19339

14712

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\ \end{align*}

7.323

19340

16519

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

7.323

19341

4954

\begin{align*} 2 \left (-x^{2}+1\right ) y^{\prime }&=\sqrt {-x^{2}+1}+\left (x +1\right ) y \\ \end{align*}

7.325

19342

18590

\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\ \end{align*}

7.325

19343

11962

\begin{align*} y^{\prime }&=\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 y^{2} x^{2}+7 x y^{2}}{x} \\ \end{align*}

7.326

19344

22981

\begin{align*} y^{\prime }-6 y&={\mathrm e}^{6 t} \\ y \left (0\right ) &= 1 \\ \end{align*}

7.328

19345

15905

\begin{align*} y^{\prime }+2 y&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= 1 \\ \end{align*}

7.332

19346

5078

\begin{align*} 2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\ \end{align*}

7.333

19347

24520

\begin{align*} 4 y+y^{\prime \prime }&=8 \\ \end{align*}

7.335

19348

15922

\begin{align*} y^{\prime }&=\frac {y}{1+t}+4 t^{2}+4 t \\ y \left (1\right ) &= 10 \\ \end{align*}

7.339

19349

1695

\begin{align*} {\mathrm e}^{y x} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{y x}+3 x \right ) y^{\prime }&=0 \\ \end{align*}

7.340

19350

8873

\begin{align*} L y^{\prime }+R y&=E \sin \left (\omega x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

7.340

19351

15034

\begin{align*} y^{\prime }&=\frac {2 y-x -4}{2 x -y+5} \\ \end{align*}

7.342

19352

19750

\begin{align*} \theta ^{\prime \prime }-p^{2} \theta &=0 \\ \end{align*}

7.344

19353

7227

\begin{align*} 2 y^{\prime }&=3 \left (-2+y\right )^{{1}/{3}} \\ y \left (1\right ) &= 3 \\ \end{align*}

7.345

19354

12876

\begin{align*} a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime }&=0 \\ \end{align*}

7.345

19355

11921

\begin{align*} y^{\prime }&=-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \\ \end{align*}

7.346

19356

11412

\begin{align*} y^{\prime } x -y-\sqrt {x^{2}+y^{2}}&=0 \\ \end{align*}

7.347

19357

19331

\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}

7.348

19358

3673

\begin{align*} y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\ \end{align*}

7.350

19359

9051

\begin{align*} y^{\prime }&=k y \\ \end{align*}

7.355

19360

22757

\begin{align*} x^{2} y^{\prime \prime }+y&=16 \sin \left (\ln \left (x \right )\right ) \\ \end{align*}

7.356

19361

27644

\begin{align*} y^{\prime \prime }-4 y^{\prime }+8 y&={\mathrm e}^{2 x}+\sin \left (2 x \right ) \\ \end{align*}

7.356

19362

5354

\begin{align*} {y^{\prime }}^{2}&=a \,x^{n} \\ \end{align*}

7.361

19363

16142

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=-2 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

7.363

19364

18848

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

7.364

19365

21617

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

7.365

19366

24798

\begin{align*} 4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}

7.365

19367

27712

\begin{align*} y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-2 \left (-1+x \right ) y&=0 \\ \end{align*}

7.371

19368

12045

\begin{align*} y^{\prime }&=\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )} \\ \end{align*}

7.372

19369

12223

\begin{align*} y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 y^{2} x^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \\ \end{align*}

7.373

19370

24003

\begin{align*} y^{\prime \prime \prime }-y&=x^{n} \\ \end{align*}

7.377

19371

20270

\begin{align*} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y+\sin \left (x \right ) \\ \end{align*}

7.379

19372

19895

\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}

7.382

19373

2533

\begin{align*} y^{\prime }&=t^{2}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

7.384

19374

27776

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

7.384

19375

14538

\begin{align*} y^{\prime }&=\frac {x y}{x^{2}+1} \\ y \left (\sqrt {15}\right ) &= 2 \\ \end{align*}

7.390

19376

27729

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*}

7.395

19377

21607

\begin{align*} y^{\prime }&=\sin \left (x +y\right ) \\ \end{align*}

7.397

19378

15813

\begin{align*} y^{\prime }&=2 y \left (1-y\right ) \\ \end{align*}

7.398

19379

9242

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\ \end{align*}

7.401

19380

1176

\begin{align*} y^{3}+y^{\prime }&=0 \\ \end{align*}

7.402

19381

7149

\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ \end{align*}

7.402

19382

12201

\begin{align*} y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\ \end{align*}

7.403

19383

1553

\begin{align*} y^{\prime }+\frac {4 y}{-1+x}&=\frac {1}{\left (-1+x \right )^{5}}+\frac {\sin \left (x \right )}{\left (-1+x \right )^{4}} \\ \end{align*}

7.404

19384

22567

\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}

7.404

19385

9236

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\ \end{align*}

7.408

19386

12033

\begin{align*} y^{\prime }&=\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\ \end{align*}

7.408

19387

22026

\begin{align*} y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\ y \left (2\right ) &= -5 \\ \end{align*}

7.408

19388

25658

\begin{align*} y^{\prime }+20 y&=24 \\ \end{align*}

7.408

19389

5180

\begin{align*} \left (1-x^{2} y\right ) y^{\prime }+1-x y^{2}&=0 \\ \end{align*}

7.409

19390

11876

\begin{align*} y^{\prime }&=\frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}} \\ \end{align*}

7.411

19391

19997

\begin{align*} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\ \end{align*}

7.411

19392

6567

\begin{align*} \operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime }&=0 \\ \end{align*}

7.414

19393

15329

\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}

7.414

19394

20482

\begin{align*} -y^{\prime } x +y&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

7.417

19395

15071

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=2 \\ \end{align*}

7.419

19396

18576

\begin{align*} 2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align*}

7.419

19397

21669

\begin{align*} x^{4} \left (x^{2}+1\right ) \left (-1+x \right )^{2} y^{\prime \prime }+4 x^{3} \left (-1+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=1\).

7.422

19398

15501

\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*}

7.424

19399

18069

\begin{align*} x -y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}

7.424

19400

26628

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y&=0 \\ \end{align*}

7.427